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Physics and Astronomy

Quantum Systems and Nanomaterials Group

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Former research interests

The Physics of Phonons

My research work in the 1970's was concentrated on the study of lattice thermal conductivity of insulators and semiconductors, including the following theoretical approaches: Relaxation time methods; Complementary variational principles; Green's function method; and Zwanzig-Mori projection operator method. I have developed a model relaxation time approach for lattice thermal conductivity. This development has been acknowledged by Callaway as one of the leading works in this field after his own pioneering work. I have also developed a method for calculating sequences of complementary variational principles (i.e. a sequence of lower bounds and a sequence of upper bounds) for the problem of lattice thermal conductivity. This is a general method for solving any mathematical problem which can be expressed in the form of a linearised equation of Boltzmann type. My recent interest includes studies of hot-phonon relaxation in semiconductors and quantum wells, an effect which takes place femto-seconds after laser excitation of such systems and are very important in controlling device performance. I have written a post- graduate book entiled
"The Physics of Phonons" , published in 1990 by Adam Hilger (Bristol).

The Physics of Electrons

Since the mid 1970's I have concentrated on theoretical studies of (a) atomic structure, (b) ground state properties, (c) electronic states, (d) photoemission, (e) optical absorption, (f) tunnelling, (g) impurity and defect electron states in solids, (h) theory of Schottky barriers at metal-semiconductor interfaces, and (i) first-principles calculations of phonon frequencies in bulk and at surfaces. These studies include a variety of theoretical techniques, such as tight-binding, empirical pseudopotential, and ab-initio pseudopotential methods. I am one of the few researchers outside USA to develop from scratch the self-consistent pseudopotential method for studying ground state and electronic properties of solids, surfaces, superlattices, metal-semiconductor interfaces, and calculation of phonons from first-principles. For carrying out these studies we have developed both a static or Hamiltonian approach (the Kohn-Sham method) and a dynamic or Lagrangian approach (the Car-Parrinello method). Occupied electronic states are studied using the local density approximation (thus the Lagrangian approach becomes ab-initio molecular dynamics approach). In order to study excited states in semiconductors and at their surfaces we have recently developed the application of a simple, practical, but physically appealing GW scheme for the self-energy operator. In our latest development both electronic eigen solutions and equilibrium atomic geometries are calculated by employing conjugate gradient schemes. Although I am engaged in a number of projects, the most challenging of my projects is modelling of metal-semiconductor interfaces and development of a theory of Schottky barrier formation.

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